Thursday, September 24, 2009

The Oyster has been immersed in two things lately: (1) maths, and (2) writing books. I want to note down some of this stuff before I forget it, because it's cool.

Maths

Following on from this post, the 1 2 3 5 4 thing sorted itself out pretty quickly (without intervention, incidentally). The synaesthesia receded in importance, and the Numberjacks mania played itself out. So, thankfully, did the bit with me writing out pages full of numbers for the Oyster to colour in. He occasionally does that himself these days. Sometimes he just does the multiples of 11, because he likes them. He went through a brief phase of writing out the times table (or as he put it, a row of "counting in ones", a row of "counting in twos", a row of "counting in threes", and so on), but that petered out fairly quickly. He knows most of the products up to around 100, I think.

He spent a week or two as an infinity denier. At first he decided that the highest number was called Niall (love that!), and that Niall plus 1 was 0. I think he now gets that you can never stop counting. He's interested in very large numbers. He likes billions and trillions and quadrillions and bazillions. I like the way that even though a bazillion doesn't exist, we can still make statements about it (e.g. it's even, it's a multiple of 10, it's a positive integer greater than a trillion, it's 1 followed by a multiple of 3 zeroes, and so on).

He knows that there are numbers between the integers, but we haven't really got into how that works yet.

He's reasonably solid on place value, as far as I can tell. Sometimes he writes out columns of numbers where column 1 is the numbers from 1 to 9, column 2 is 10 20 30 ... 90, column 3 is 100 200 300 ... 900, and so on. Sometimes we multiply numbers by 2 until we exhaust first his capacity, then mine (to do it without stopping to concentrate or write it down, I mean), then my calculator's (to display the result without resorting to scientific notation). He really likes asking me sums, or having a repeated joke such as "What's 55 plus 55 - is it tenty-ten? *giggle*"

Did you know that if x squared is y, then (x + 1) squared is y + 2x + 1? (For example, 6 squared is 36, and 7 squared is 36 + 12 + 1.) I didn't, until the Oyster got me doing squares in my head (while driving - not recommended!) up to 30 or so.

He has the hang of the number line, and can add and subtract small positive and negative numbers fairly easily, particularly if he has a number line in front of him. His mental arithmetic above 0 is pretty good. "What's 54 plus 35 ... is it 89?" he'll say, or "Is 88 plus 88 176?" Béar Eile (his special bear) turned 107 at the weekend, and he accurately added up the ages of all the humans in the house, then had a reasonable stab at calculating the difference between that number (75, for those following along at home) and 107.

Today's little nugget was when he was counting a page full of pictures, and he counted across the first row of twelve, began to count the second row, then checked himself and counted the number of rows instead. "Four twelves, what's that? Is it 48?"

He has some grasp of bases other than 10. When he was talking to Niall about them, he observed that for base 5, you only need the numbers 0 to 4 to write any number. When the Erisian was visiting, he taught the Oyster about binary - and showed him how to count to 31 on the fingers of one hand. I'm not sure how much of that stayed in, but he appeared to grasp it - and at least when he encounters it again it'll be familiar.

It was also while the Erisian was here that the Oyster asked, "Do all the twelve numbers do that thing where ... like, 1 plus 1 is 2, and 1 2 is 12; 2 plus 2 is 4, and 2 4 is 24?" Turns out they do, as long as you put the original number in the tens column and add it to whatever's there (e.g. 5 plus 5 is 10, and (5+1) 0 is 60; 6 plus 6 is 12, and (6 + 1) 2 is 72). Not sure how far up that goes. But we were very tickled that he'd noticed.

My parents got him a 1st class maths book as a present. He takes it out a couple of times a week and does a few pages of exercises. He's done them easily, so far, once I've read the instructions to him. Mostly, what confuses him is the part about being required to demonstrate how he's getting his answers. The first module dealt exclusively with addition of two numbers with an answer of 10 or less. A few pages later, there were sums with an answer of 11 or 12. Later still, the sums had answers of 13 or 14. He's now even done some where you add more than two numbers. He flipped to the middle of the book and found sums demonstrating place value with columns of dots, and sums to calculate how much change you'd have from 10 cents if you bought an item with a given price.

If he were in school, this would be the book for his third year. To me, this seems generally supportive of our hypothesis that being home-educated is unlikely to lead to academic disadvantage for our children. Actually, what I love about the Oyster's engagement with maths is that from my perspective, it seems that he's Doing Numbers in exactly the same way that he Did Trains a while ago, or Did Robin Hood earlier this year. He's following what fascinates him, in other words, which is the key idea. It's kind of thrilling to see it in action.

Books

There is rather less to say about books, other than that the Oyster is an enviably prolific author. He has written books about Robin Hood, books about dragons, books about trains, monsters, aliens, dinosaurs, knights, numbers. He has written books in A4 and A5 size (stapled by patient relatives, often with several stapled booklets taped together); he has written tiny little books in A7 size (painstakingly assembled by me - so far, a 100-pager and a 256-pager, with cardboard covers).

By "written", I mean that generally he draws the pictures first, then asks for the spellings to write the words (which often go in speech bubbles). Recently, he has been asking only for the words he doesn't know - he can do "the", "and", "of", "book", among others, without assistance. Also, I've adopted the strategy of writing out the phrase he wants on a scrap piece of paper for him to copy, which is less hair-tearingly tedious than calling out the letters in batches of three or four.

Before beginning to write, however, the srs bsns of putting the book together must be completed. Page numbers are very important. So are front and back covers, end-papers, and the contents page. Recently he started adding barcodes (complete with little numbers written along the top), prices, blurbs, and endorsement quotes. Some of his books have had an index.

Today's titles, as a snapshot: Elementary Trains (a present for K), Spaceman George (not sure that one went very far before being abandoned), a recipe book called Oisín's Food, and a two-part series: The Story of the Skull and Further Adventures of the Skull. These latter two were for the Boy Down the Road, who is ... ah ... very traditionally socialised, and likes weapons and fighting and horror-type stuff (but is nonetheless more or less a sweetheart). The Oyster fits his material to his readership, in other words, which I find very interesting.

Wednesday, September 23, 2009

I've been asked this more and more lately, and it comes hard on the heels of the many many entries in other people's blogs about why they chose home ed.

I find it kind of hard to answer.

On some levels, home education is a default for me, it's the no-choice no-decision option, much like school is for most people (which school might be a decision, but not whether school). It started to make visceral sense to me when I was about six.

However, when we were looking for somewhere to live, somewhere with a wide choice of schools was important, and somewhere with fairly decent schools and similar institutions, too - not stellar, necessarily, because things change and anyway parental involvement matters more than the school's position on a league table, but ok. We didn't hunt for schools and then look for houses, but we dismissed houses which weren't within easy walking distance of schools.

Because along with assuming that home education would suit me and my family best, I also assumed that I'd have to send my children, when I had them, to school. Just because people have to.

But I don't! Aren't I lucky?

And why not school? I just really don't see that it would, at present, benefit my children in any way. I have a bunch of philosophical objections to the way school as a system is set up and run, but it's still obvious that that system does benefit many adults and children for a wide variety of reasons. Just I can't see a benefit to us yet, and the benefits of what we do are blazingly obvious to me.

I also think that one of my children would be, at this stage in her life, actually damaged by almost all the school set-ups I've seen, and certainly all the ones I've seen as economically available to us. That might change; I expect as she grows older her round peggishness will gradually grow to meet school's square holishness, such that she could fit in there ok even if it didn't benefit her.

I'm glad schools are there, for those as needs 'em, because one day that might include me and mine, and it certainly includes a lot of my nearest and dearest.

Sometimes I'd like to ask them why they chose school. But it's really really rude to do so, so I don't.

Thursday, September 17, 2009

Monday, September 07, 2009

Yesterday Linnea was asked what's her favourite story, and she said "The one about the animals and the man makes a boat and the flood." And the other week I was talking to a friend about the cultural references children like ours just won't have to the same extent - we're making no effort to raise Christian or Catholic children, either at home or by sending them to schools where everyone does First Holy Communion and Confirmation and all the rest.

But I think some familiarity with the stories would be a good idea. As a child I had access to a set of American books which were wonderful; they were published by Scholastic and each one had a simple illustrated bible story in it. There were a hundred or so, I think - books a few mm thick taking up a whole shelf. I wonder whether or how I could find such a thing now?

Friday, September 04, 2009

I recently found and printed off a bunch of stuff from the CIMT's Mathematics Enhancement Programme (Primary Extension). I have no idea what's supposed to be "innovative" about it, but the children enjoy it (Linnea, who is five, tries to actually do the exercises and Emer, who is three, colours things in and cuts them out, but they both have the same print-outs, so they're happy).

Linnea likes it except for not feeling confident to read the instructions unless she's alone, and not feeling confident to do the exercises unless I say "that looks right to me, what do you think?" a lot. On the other hand, it does mean she's letting me be involved in something, which is fabulous for me. And mainly she's working through things she finds very easy usually, but doing them slowly and self-critically, with an element of checking-her-work she hasn't usually shown me.

Along with a recent tendency to do things for reward, which she never used to accept, I wonder whether she's reached a stage where she's willing to perform a bit? I mean, willing to do things explicitly knowing there's praise or not-praise at the end of it? That's a big leap for her, and I'm not sure how I feel about it.

Meanwhile, she likes and = very much but would like to introduce V and a sort of bar-less A for other values, like "kind of the same" and "not actually more but bigger anyway."